Recently, Prof. Jian Wang’s group at International Center of Quantum Materials, School of Physics, Peking University, in collaboration with Prof. X. C. Xie and Prof. Fa Wang at Peking University, Prof. Kui Jin at Institute of Physics, Chinese Academy of Sciences, Prof. Haiwen Liu at Beijing Normal University, and Prof. Yi Liu at Renmin University of China, observed the 3D superconductor to Anderson critical insulator transition and quantum Griffiths singularity in spinel oxide MgTi2O4, which paves a new path for the observation of quantum phase transitions in 3D superconducting systems and demonstrates the universality of quantum Griffiths singularity in superconductors with different dimensionalities. This article, entitled “Quantum Griffiths Singularity in a Three-Dimensional Superconductor to Anderson Critical Insulator Transition” was published in Physical Review Letters on November 26, 2024 (Phys. Rev. Lett. 133, 226001 (2024)).
Driven by quantum fluctuations, the quantum phase transition (QPT) represents zero temperature phase transition between different quantum ground states. The QPT has been observed in different physical systems, such as superconductors, quantum Hall systems, heavy-fermion materials, and ultracold atoms. Understanding the dual effect of disorder and quantum fluctuation on QPTs is a central topic in condensed matter physics. Benefiting from the strong fluctuation effect, low-dimensional superconducting systems are promising platforms to investigate the QPT. In the investigations of superconductor to metal transition in trilayer Ga films, Jian Wang’s group and collaborators discovered a new type of QPT—quantum Griffiths singularity (QGS), whose main characteristic is the divergence of the dynamical critical exponent when approaching the infinite randomness quantum critical point (Science 350, 542 (2015)). The discovery of QGS reveals the profound influence of disorder and dissipation on the QPT in two-dimensional superconductors and generalizes the universality class of QPT. Afterward, Jian Wang’s group detected the QGS and anomalous QGS under perpendicular magnetic fields (Phys. Rev. B 94, 144517 (2016); Nano Lett. 17, 6802 (2017); Nat. Commun. 10, 3633 (2019)), and the QGS under parallel magnetic fields (Phys. Rev. Lett. 127, 137001 (2021)) in various 2D superconducting systems, making the QGS a research highlight in the field of two-dimensional superconductivity. However, the experimental detection of QGS in 3D superconductors is still very challenging due to the relatively weak fluctuation effect.
Recently, Prof. Jian Wang’s group performed the systematic transport measurements at ultralow temperatures and strong magnetic fields on spinel oxide MgTi2O4 (MTO) films. The perpendicular and parallel upper critical magnetic fields are nearly isotropic, and the superconducting coherence length is much smaller than the MTO film thickness, revealing the 3D superconducting nature of MTO (Fig. 1). The superconducting state can be tuned to the insulating state by increasing the perpendicular or parallel magnetic field. Furthermore, the theoretical fitting of the insulating state in MTO reveals the fermionic nature. Thus, the MTO undergoes a 3D superconductor to fermionic insulator phase transition with increasing the magnetic field. More interestingly, the magnetoresistivity isotherms in MTO cross each other in a transition region, in stark contrast to conventional SIT characterized by a single crossing point. Based on the finite size scaling analysis, the effective critical exponent zν diverges when approaching the quantum critical point and follows the activated scaling law (here z and ν are dynamic critical exponent and correlation length exponent, respectively). The power-law fitting yields a power exponent of 0.33, demonstrating the existence of 3D QGS (Fig. 2).
Fig. 1. (a) Temperature dependence of resistivity at zero magnetic field. (b) Temperature dependence of perpendicular and parallel upper critical fields. (c) The magnetoresistivity measured at different orientations.
Fig. 2. (a) The superconductor to insulator transition under magnetic fields. (b) The magnetoresistivity isotherms cross each other in a transition region. (c) The divergence of the critical exponent approaching the quantum critical point provides evidence of the 3D quantum Griffith singularity.
In general, the fluctuation effect in superconductors can be characterized by the broadening of superconducting transition. A large transition region indicates strong fluctuation effect. The transition region of MTO is much larger than that of other 3D superconductors and even comparable to that of 2D superconductors, indicating strong fluctuation effect (Fig. 3). The theoretical analysis of the upper critical fields in MTO indicates that the MTO is a strongly disordered system and the normal state is in the vicinity of the mobility edge of Anderson localization, which is further supported by the power-law scaling of the normal state resistivity. In the critical region of Anderson localization, the Anderson localization length (correlation length) exceeds the superconducting coherence length, which enhances the fluctuation of superconducting order parameter. Moreover, the competition between the orbital order and the superconductivity further enhances the fluctuation effect in MTO. Consequently, the enhanced fluctuation effect in the Anderson critical regime leads to the observation of 3D QGS in MTO. This work not only provides a deeper understanding for the quantum dynamics in disordered physical systems, but also paves a new path for the investigation of QPT in 3D superconducting systems.
Fig. 3. (a) Overview of fluctuation effect in 2D and 3D superconductors. (b) Schematic phase diagram of superconductor and Anderson localization. (c) Orbital order in MTO.
In this work, Shichao Qi at Peking University, Prof. Yi Liu, Dr. Ziqiao Wang at Peking University and Dr. Fucong Chen at Institute of Physics, Chinese Academy of Sciences contribute equally to this work. Prof. Jian Wang, Prof. Kui Jin and Prof. Haiwen Liu are corresponding authors of this paper. This work is financially supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, Beijing National Laboratory for Condensed Matter Physics, CAS Project for Young Scientists in Basic Research, the Center for Materials Genome, Young Elite Scientists Sponsorship Program by CAST, Young Elite Scientists Sponsorship Program by BAST, and the Fundamental Research Funds for the Central Universities.
Paper link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.226001
